Adding and Subtracting Polynomials

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, $$3x^2 + 2x - 5$$ is a polynomial.

Count the number of distinct terms separated by '+' or '-' signs. For example, in $$3c^5 - 6c^2 + 8c^7 + 3c$$ , there are 4 terms.

The degree of a polynomial is the highest power of the variable in the expression. For example, the degree of $$4x^5 + 2x^3 - x + 7$$ is 5.

Combine like terms by adding their coefficients. For example, to add $$(4x - 2x^3) + (5x^3 - 4x + 5)$$ , combine like terms to get $$3x^3 + 5$$ .

Like terms are terms that have the same variable raised to the same power. For example, $$2x^2$$ and $$5x^2$$ are like terms.

The result is $$11x^4 + 2x^2 + 14x$$ .

Subtract by distributing the negative sign and then combining like terms. For example, $$(5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2$$ .

A coefficient is a numerical factor in a term of a polynomial. For example, in $$5x^3$$ , 5 is the coefficient.

The standard form of a polynomial is written in descending order of the degree of its terms. For example, $$4x^3 + 2x^2 - x + 7$$ .

The leading term is the term with the highest degree in a polynomial. For example, in $$3x^4 + 2x^3 - x + 5$$ , the leading term is $$3x^4$$ .